These are the times when you are not able to state anything definitively. If, given a hypothesis, you are able to say with a high degree of certainty either "yes" it is true or (paradoxically) "no" it is not, these are both regarded as positive results. If you are unable to say "yes" or "no" then that is a negative result. In traditional hypothesis testing a positive result is when you have rejected the null hypothesis and hence decided you have evidence for the alternative hypothesis; a negative result is when the test is non significant. In this case there is no definitive "no", merely "yes" and "not proven". A negative result may mean there is no effect, or that your study did not have sufficient statistical power.
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